A bicycle tire company performed a web-based study of a popular tire retail price over time. The study indicated that price is set at $16.00 per tire, it was expected to increase to $19.00 over the next 5 years a. Determine the annual rate of inflation over 5 years to increase the price from $16.00 to $19.00. b. Determine the market interest rate that must be used in economic equivalence computations if inflation is considered and an 8% per year real interest rate is expected by this company.

To determine the annual rate of inflation over 5 years from a price increase of $16.00 to $19.00, you can use the formula for the compound annual growth rate (CAGR):

a. Annual rate of inflation over 5 years:

Initial Value = $16.00

Final Value = $19.00

Number of Periods = 5

CAGR=( Final Value / Initial Value ) ^{1 / Number of Periods} - 1

CAGR=( 19.00 / 16.00 ) ^1/5 − 1

CAGR = 0.0387 or 3.87% per year

b. To determine the market interest rate considering inflation and an 8% per year real interest rate expected by the company, you need to use the Fisher equation:

Nominal Interest Rate = ( 1 + Real Interest Rate ) × ( 1 + Inflation Rate ) − 1​

Given:

Real Interest Rate = 8% per year (0.08)

Inflation Rate (from part a) = 3.87% per year (0.0387)

Nominal Interest Rate = ( 1 + 0.08 ) × ( 1 + 0.0387 ) − 1

Nominal Interest Rate = 1.08 × 1.0387 − 1

Nominal Interest Rate = 1.120996 − 1

Nominal Interest Rate = 0.120996 or 12.10% per year 

Therefore, considering inflation and the company's expected real interest rate of 8% per year, the market nominal interest rate would need to be approximately 12.10% per year.